A runner is jogging in a straight line at a steady vr= 2.2 km/hr. When the runner is L= 4 km from the finish line, a bird begins flying straight from the runner to the finish line at vb= 6.6 km/hr (3 times as fast as the runner). When the bird reaches the finishline, it turns around and flies directly back to the runner.
Q1:What cumulative distance does the bird travel? Even though the bird is a dodo, assume that it occupies only one point in space (a “zero” length bird), travels in a straight line, and that it can turn without loss of speed.
Q2: After this first encounter, the bird then turns around and flies from the runner back to the finish line, turns around again and flies back to the runner. The bird repeats the back and forth trips until the runner reaches the finish line. How far does the bird travel from the beginning (including the distance traveled to the first encounter)?I CANT UNDERSTAND please someone explain to me thank you!
part 2 of this question is easier than part 1.
For part 2, just figure how long it takes the runner to finish the race. At 2.2 km/hr, it will take 4/2.2 = 1.81 = 20/11 hours. Since the bird is flying at 6.6 km/hr for that whole time, it files 6.6 * 20/11 = 12 km
The hard part is figuring out the distance to that first encounter.
Since the bird flies 3 times as fast as the runner, when the bird gets to the finish line, the runner is only 1/3 of the way there, so the distance between the bird and the runner is 8/3 km. So, since the bird flies 3 times as fast, it will cover 3/4 of that distance, or 2 km. So its total flight is 4+2=6 km.
Q1: To find the cumulative distance traveled by the bird, we need to consider the distance it travels to reach the finish line, plus the distance it travels back to the runner.
First, let's calculate the time it takes for the bird to reach the finish line. We know that the bird is flying at a speed of vb= 6.6 km/hr, and the distance to the finish line is L= 4 km. We can use the formula distance = speed * time to find the time it takes for the bird to reach the finish line.
Time taken to reach the finish line = Distance / Speed
= 4 km / 6.6 km/hr
Next, we need to calculate the time taken for the bird to travel back to the runner. The bird is now flying at the same speed vb= 6.6 km/hr, but the distance it has to cover is now twice the original distance (2L).
Time taken to reach the runner = (2L) / vb
= 2 * 4 km / 6.6 km/hr
Now, to find the cumulative distance traveled by the bird, we add the distance traveled to reach the finish line and the distance traveled back to the runner.
Cumulative distance traveled by the bird = Distance to finish line + Distance from finish line back to runner
= 4 km + 2 * 4 km
= 12 km
Therefore, the cumulative distance traveled by the bird is 12 kilometers.
Q2: In this scenario, the bird repeats the back and forth trips until the runner reaches the finish line. To calculate the total distance traveled by the bird from the beginning, we need to find the distance for each round trip and sum them up.
In each round trip, the bird covers a distance of 2L. The runner is initially at a distance of L= 4 km from the finish line.
The number of round trips the bird will make is determined by the runner's distance to the finish line (L) and the distance covered in each round trip (2L).
Number of round trips = L / 2L
= 1/2
Since the bird travels 2L in each round trip, the total distance traveled by the bird from the beginning is given by:
Total distance = Number of round trips * Distance per round trip
= 1/2 * 2L
= L
= 4 km
Therefore, the bird travels a total distance of 4 kilometers from the beginning (including the distance traveled to the first encounter).